Article Dans Une Revue Journal of Statistical Mechanics: Theory and Experiment Année : 2021

Nishimori meets Bethe: a spectral method for node classification in sparse weighted graphs

Résumé

This article unveils a new relation between the Nishimori temperature parametrizing a distribution P and the Bethe free energy on random Erdős-Rényi graphs with edge weights distributed according to P. Estimating the Nishimori temperature being a task of major importance in Bayesian inference problems, as a practical corollary of this new relation, a numerical method is proposed to accurately estimate the Nishimori temperature from the eigenvalues of the Bethe Hessian matrix of the weighted graph. The algorithm, in turn, is used to propose a new spectral method for node classification in weighted (possibly sparse) graphs. The superiority of the method over competing state-of-the-art approaches is demonstrated both through theoretical arguments and real-world data experiments.

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Dates et versions

hal-03354394 , version 1 (24-09-2021)

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Lorenzo Dall'Amico, Romain Couillet, Nicolas Tremblay. Nishimori meets Bethe: a spectral method for node classification in sparse weighted graphs. Journal of Statistical Mechanics: Theory and Experiment, 2021, 2021 (9), pp.093405. ⟨10.1088/1742-5468/ac21d3⟩. ⟨hal-03354394⟩
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